Presentations of metacyclic groups

DOI10.1017/S0004972700045500zbMath0245.20016MaRDI QIDQ5656926

Bruce Whitfield King

Publication date: 1973

Published in: Bulletin of the Australian Mathematical Society (Search for Journal in Brave)

Mathematics Subject Classification ID

Generators, relations, and presentations of groups (20F05) Finite nilpotent groups, (p)-groups (20D15)

Related Items

Groups in which every non-abelian subgroup is self-centralizing ⋮ Metacyclic p-groups and their conjugacy classes of subgroups ⋮ Groups with few non-normal subgroups ⋮ The multiple holomorph of split metacyclic p-groups ⋮ Skew-morphisms of cyclic \(p\)-groups ⋮ \(p\)-groups with few conjugacy classes of normalizers. ⋮ On a duality for codes over non-abelian groups ⋮ Finitely generated groups with commutator group of prime order ⋮ Projective characters of metacyclic p-groups ⋮ Finite metacyclic1‐eand1‐agroups ⋮ Groups with C-closed noncyclic subgroups ⋮ On the metacyclic 2-groups whose abelianizations are of type \((2, 2^n)\), \(n\geq 2\) and applications ⋮ Conjugacy classes of maximal cyclic subgroups of metacyclic \(p\)-groups ⋮ The Amit-Ashurst conjecture for finite metacyclic \(p\)-groups ⋮ Maximal Abelian and minimal nonabelian subgroups of some finite two-generator \(p\)-groups especially metacyclic. ⋮ The modular group algebra problem for metacyclic 𝑝-groups ⋮ Absolutely split metacyclic groups and weak metacirculants ⋮ Finite 2-generator equilibrated \(p\)-groups. ⋮ The subgroups of finite metacyclic groups ⋮ An Elementary Classification of Finite Metacyclic p-Groups of Class at Least Three ⋮ A Classification of Metacyclic 2-Groups ⋮ Powerful \(p\)-groups have non-inner automorphisms of order \(p\) and some cohomology. ⋮ Noether's problem for metacyclic \(p\)-groups ⋮ Faithful irreducible projective representations of metabelian groups ⋮ A classification of finite metahamiltonian \(p\)-groups ⋮ Powerfully nilpotent groups of rank 2 or small order ⋮ On generalized Dedekind groups. ⋮ Finitep-Groups and Centralizers of Noncentral Elements ⋮ Finite separable metacyclic 2-groups. ⋮ Finite p-groups all of whose proper subgroups of class 2 are metacyclic ⋮ Split metacyclic \(p\)-groups that are \(A\)-\(E\) groups ⋮ Metacyclic groups

Cites Work

• Nonnormal subgroups of \(p\)-groups.
• On the Isomorphisms of Two Metacyclic Groups
• Endliche Gruppen I

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